FRM Part I · FRM Exam Part I · Measuring Return, Volatility, and Correlation
Concordant and discordant pairs are used to compute Kendall's tau. For a sample of 6 paired observations (15 distinct pairs), 12 pairs are concordant and 3 are discordant, with no ties. What is Kendall's tau?
Kendall's tau is 0.60. It equals concordant pairs minus discordant pairs divided by total pairs: 12 minus 3 is 9, divided by 15. The common error is to report the share of concordant pairs, 0.80, which ignores the penalty for discordant pairs.
- A0.20
- B0.60Correct
- C0.80
- D0.75
Explanation
Tau = (concordant - discordant) / total pairs = (12 - 3)/15 = 9/15 = 0.60. The 0.80 option is the proportion concordant (12/15), which ignores the subtraction of discordant pairs. The 0.75 option divides by the wrong base (12).
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